An overview of interferometric techniques used in the prior art is provided by J. E. Greivenkamp and J. H. Bruning in Chapter 14 of "Optical Shop Testing", 2nd Ed., J. Wiley pub, edited by D. Malacara. These techniques are used extensively for high precision, non-contact metrology. With careful control of environmental conditions, measurement precision to the nanometer scale or below is possible with these techniques; however, residual measurement errors may occur, with external vibration being the single largest cause of such residual measurement errors. For most commercial profilers, control of environmental conditions requires, at a minimum, a passively isolated instrument; however, passive vibration isolators perform poorly against low frequency vibrations. Prior art attempts at solving these problems have not been completely satisfactory with having involved such approaches as changing the phase extraction algorithm, as disclosed in articles by P. de Groot, "Vibration in phase shifting interferometry", J. Opt. Soc. Am. A 12, 354-365 (1995), C. T. Farrell and M. A. Player, "Phase-step insensitive algorithms for phase-shifting interferometry", Meas. Sci. Tech. 5, 648-652 (1994), and I. Kong and S. Kim, "General algorithm of phase-shifting interferometry by iterative least-squares fining", Opt. Eng. 34, 183-188 (1995). This prior art approach, while not completely satisfactory, can provide some useful reduction in vibration sensitivity. The prior art approaches suggested by Farrell and Player, and more recently Kong and Kim, show significant insensitivity to small amplitude vibrations if the phase shift is assumed to be constant across the field and a least squares fit to this constraint is performed in the analysis of the interferogram. Large amplitude vibrations, however, can make it impossible to overcome a phase ambiguity in the analysis that the authors attempt to currently resolve by assuming the phase shifts are unidirectional. Another prior art approach, which is not completely satisfactory as well, is discussed in an article by J. L. Seligson, C. A. Callari, J. E. Greivenkamp, and J. W. Ward entitled "Stability of a lateral-shearing heterodyne Twyman-Green interferometer", Opt. Eng. 23, 353-356 (1984) in which the authors discuss using a separate interferometer to measure the true phase shifts during interferogram acquisition. This, in principle, can substantially reduce vibration sensitivity even for large amplitude disturbances, but it is expensive and difficult to implement, requiring a stabilized laser, precision optics and sophisticated electronics to measure the true motion of the phase shifter. As a laboratory tool it may suffice, however, it is not a commercially viable solution. Another prior art approach, with results similar to those discussed in Seligson is disclosed in U.S. Pat. No. 5,410,405, to Schultz et. al. which discloses using a homodyne interferometer to achieve similar motion measurements as Seligson above. Recent work on the vibration sensitivity of various algorithms, such as discussed in the above de Groot article, shows, however, that all algorithms will be most sensitive to vibrational frequencies at half the data acquisition rate since vibrations at this frequency produce phase variations which are indistinguishable from phase variations due to surface features. The sampling rates are driven by video with cameras most often being used to sample the interferogram, and that makes 30 Hz very typical: thus vibrations at 15 Hz and lower cause the bulk of the problems. Active vibration compensation devices, such as commercially available from Newport Corp. (Irvine Calif.) are expensive and can compensate for only a limited vibration amplitude range, and do not correct for deficiencies in the apparatus itself, such as scanning nonlinearities. Another prior art approach is discussed in a paper presented by J. A. Meiling, entitled "Interferometric Metrology of Surface Finish Below 1 Angstrom RMS", which appears in the April 1992 proceedings of the ASPE spring topical meeting on precision interferometric metrology. In this paper Meiling presented results based on massive data averaging. This methodology, however, is extremely slow and systematic errors will not average out.
Another prior art approach, called instantaneous phase detection, such as described by R. Smythe and R. Moore, in "Instantaneous phase measuring interferometry", Opt. Eng. 23, 361-364 (1984) and in U.S. Pat. Nos. 4,653,921 and 4,624,569 to Kwon, is fast, thereby "freezing out" the vibration effects however, it requires a minimum of 3 detectors (typically four to achieve resolutions typically expected for an interferometric instrument) and these detectors must be prealigned spatially to sub-pixel accuracy and have the identical environmental characteristics if the operating conditions are not to be too restrictive. The image must be split between each detector and the phase shifted optically with a phase retarder, whose retardation must be either uniform across the field or known as a function of field. The individual pixel gains and offsets of each detector must be either identical (almost impossible) or mapped; and the images must also be acquired simultaneously, requiring the equivalent of 3 or 4 framegrabbers all synchronously operated. These problems and the associated costs make this prior art method extremely difficult to implement beyond single point detection applications described in the articles cited.
The practical difficulties of increasing the speed of data acquisition have even made even this apparent "straightforward" method relatively difficult, especially since profiling applications rarely wish to sacrifice lateral resolution for speed. High speed, high resolution sensors are rare and extremely expensive. For example, a 210 Hz, 1024 pixel.times.1024 pixel, camera produced by the David Sarnoff Labs (the SAR 1024) has 32 parallel output taps and costs over $200,000. The high speed requirement directly impacts the camera signal to noise ratio, forcing most of these cameras into a multiple output (multitapped) configuration. The multitapped nature of these cameras then requires a sophisticated data acquisition device that is incompatible with typical commercial framegrabbers. A custom acquisition system for the SAR 1024 called the RAM CUBE was built by TRW and costs as much as the camera. Although, other commercially available high speed, high resolution cameras may be less costly, it has been found that incorporating high speed, high resolution cameras into practical commercially viable products at the present time, apart from any other problems, is simply not cost effective.
The present invention overcomes these problems in the prior art and allows the use of inexpensive low frame rate, high density cameras to achieve vibration insensitivity almost as good as that achievable with a single camera of comparable density and speed. Furthermore, the presently preferred method of the present invention is applicable to many different types of interferometric systems, such as phase shifting interferometers, coherence scanning interferometers or long equivalent wavelength interferometers. In addition, the presently preferred method of the present invention is also capable of correcting for instrumental deficiencies, such as errors in the phase shifting apparatus, without the need for additional distance measuring interferometers, thereby reducing cost.